Imaging the Stereodynamics of Cl + CH4(ν3 = 1): Polarization

Letter pubs.acs.org/JPCL

Imaging the Stereodynamics of Cl + CH4(ν3 = 1): Polarization Dependence on the Rotational Branch and the Hyperfine Depolarization Huilin Pan,† Jiayue Yang,†,§ Fengyan Wang,†,∥ and Kopin Liu*,†,‡ †

Institute of Atomic and Molecular Sciences (IAMS), Academia Sinica, P.O. Box 23-166, Taipei, Taiwan 10617 Department of Physics, National Taiwan University, Taipei, Taiwan 10617

‡

ABSTRACT: The transition state in the Cl + CH4 reaction is of Cl−H−C collinear geometry, which serves as the bottleneck to reaction. When the reactant CH4 is antisymmetrically stretch-excited to ν3 = 1 by absorbing a linearly polarized photon, all four C−H bonds are collectively excited, and any one of the H atoms could be attacked by the Cl atom. At first sight, it is not obvious how an excited spherical-top molecule like CH4 is aligned and what consequences will be on chemical reactivity by polarizing the CH4 reagents. As shown here, an enormous steric effect on reactivity is observed, which depends sensitively on the selected rotational states. By exploiting various rotational branches in optical excitation, we quantify the degree of stereospecificity for a few lowest rovibrational states of the aligned CH4(ν3 = 1) reagents, as well as account for the hyperfine depolarization factor. This information lays the foundation for a full stereorequirement study of the Cl + CH4(ν3 = 1) reaction. SECTION: Kinetics and Dynamics

I

n a series of recent papers,1−4 our laboratory reported a detailed study of the stereodynamics of the alignedCHD3(ν1 = 1) + Cl reaction. A pronounced dependence of reactivity on the polarization direction of the infrared (IR) laser (in preparing the vibrationally excited CHD3 reactants) was revealed, indicative of the asymptotically aligned CHD3 being largely retained in space as the two reactants collide. On the basis of the theoretical framework developed by Aldegunde et al.,5 a full set of the polarization-dependent differential cross sections (PDDCSs) was recovered,2,3 which enabled us to delineate a complete three-dimensional characterization of the stereorequirement of this benchmark polyatomic reaction. More recently, through symmetry consideration, Wang et al. also demonstrated an experimental scheme to unfold the impact parameter averaging in collisions from such polarization-dependent measurements.4 In those reports, the rotational branch of R(0) was employed in the CHD3(ν1 = 1 ← 0) transition. Therefore, the rotational angular momentum N of the IR-excited CHD3(ν1 = 1, |NK⟩ = | 10⟩) reactants is preferentially aligned in a plane perpendicular to the IR linear polarization direction due to the ΔmN = 0 optical selection rule.6 [We used N here instead of the conventional J for the rotational quantum number so that it is in line with the CH4 notation later.] Because the CHD3(ν1 = 1 ← 0) transition is of a parallel type (ΔK = 0),6 the excited C− H bond (where the transition moment lies) is also aligned and orthogonal to N. An interesting question then arises: Is the observed stereospecificity in the Cl + CHD3(ν1 = 1,|10⟩) reaction due primarily to the aligned C−H bond (chemically more intuitive2,4,7) or the N alignment (more natural in the theoretical framework5,8)? A sensible approach seems to © 2014 American Chemical Society

perform the same measurements using instead the Q(1)branch excitation, for which both the C−H bond and the N vector of the prepared CHD3(ν1 = 1, |1 ± 1⟩) reactants are preferentially aligned along the , field of the IR laser.1,9,10 To our surprise, the results are not obvious at all; a more detailed account will be presented in the near future. To shed more light on the mechanistic origin of the steric effects from a different perspective, we turned our attention to the Cl + aligned-CH4(ν3 = 1) reaction. A number of reasons prompted us to carry out this investigation. First, Simpson et al. already observed an intriguing and subtle polarization effect in a pioneering study of this reaction by probing the HCl(ν = 1, J = 1) products, using the PHOTOLOC approach.10 The combination of the crossed-beam with a time-sliced product imaging technique would offer a better opportunity to reveal the alignment effects in full, as demonstrated in the Cl + CHD3(ν1 = 1) reaction.2,3 Second, all four hydrogen atoms are collectively excited in CH4(ν3 = 1), in contrast to the local C− H bond excitation in CHD3(ν1 = 1). Third, the rotational level structure of CH4 (a spherical top) differs from that of a symmetric-top as CHD3. Thus, contrasting the polarization results from different rovibrational states of the two molecules might offer a fresh view as to the underlying mechanism. Our aim is to gain deeper insights into stereorequirements by measuring a complete set of PDDCSs in the title reaction to contrast with those in the Cl + CHD3(ν1 = 1) reaction.2−4 To Received: October 1, 2014 Accepted: October 21, 2014 Published: October 21, 2014 3878

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achieve that, however, a number of experimental questions need to be addressed first. (1) Which rotational branch shall we use to prepare the excited CH4(ν3 = 1) that would reveal the steric effect most clearly? (2) Due to the presence of the nuclear spin of hydrogen atoms (IH = 1/2) and the nuclear spin-rotational couplings, the initially IR-aligned rotational angular momentum will be depolarized with time. Then, what is the optimal delay time to interrogate the stereodynamics in this IR-pump and UV-probe experiment? (3) How can one account for the associated hyperfine depolarization effects? In this Letter, we try to seek the answers to these questions. The rovibrational energy level structures of CH4 and the four optical transitions used in this study have been depicted previously.11 The antisymmetricstretching mode (ν3) of CH4 is triply degenerate, accompanied by one quantum of the vibrational angular momentum, l = 1, for ν3 = 1. Denoting J(N) as the total (rotational) angular momentum quantum number, one has J = N + l. The rotational states of CH4(ν3 = 1) prepared by the P(1), Q(1), R(0), and R(1) branches will then be designated as |J N l⟩ = |0 1−1⟩, |1 1 0⟩, |1 0 1⟩, and |2 1 1⟩, respectively. The crossed-beam, product-imaging setup was essentially the same as that in the previous reports.1−4 In brief, two doubleskimmed pulsed beams, a discharge-generated Cl atom beam (a mixture of 5% Cl2 in Ne at 6 atm) and a neat CH4 beam, were crossed in a differentially pumped chamber. A linearly polarized, tunable IR OPO/A (optical parametric oscillator/ amplifier) tuned to the ν3 = 1 ← 0 transition was directed to the crossing region of the two molecular beams to excite a fraction of CH4 reactants to a single rovibrational excited state.11 After the collisions, the ground-state CH3(00) products were detected by a (2 + 1) resonance-enhanced multiphoton ionization (REMPI) method12−16 and recorded by a timesliced, velocity imaging technique.17 To interrogate the effects of antisymmetric-stretching excitation, the product images were acquired as a pair of IR-on and IR-off. Two sets of measurements were performed to search for the “best” conditions in the study of aligned reactions. First, for a given rotational branch and at a fixed IR−UV delay time, the dependences of image signals on the IR polarization direction were measured under two molecular beam geometries, with the initial relative velocity vector (k) being parallel (the φ geometry) or perpendicular (the α geometry) to the IR laser propagation axis.1−4 Second, to find out the IR−UV delay time to be used in the full alignment experiment, the temporal profiles of the image signals under two IR polarization directions, parallel (∥) or perpendicular (⊥) to k,1,4 were measured. By analyzing the temporal profiles, we also deduced the hyperfine depolarization correction factor at the optimal delay of the two lasers. Figure 1a exemplifies four raw images, with the R(0) excitation, of the CH3(00) products in the Cl + CH4 reactions at Ec = 4.8 kcal mol−1. The IR-off image is characterized by a backward-dominant feature, energetically corresponding to the (νCH3,νHCL) = (00,0)g product pair from the ground-state reaction, Cl + CH4(ν = 0).18 Additional features show up in the three IR-on images, signifying the effects of the antisymmetricstretching excitation of CH4 reactants. Energetically, they were readily assigned to the (00,0)s and (00,1)s product pairs.16 The subscripts “g” and “s” denote the ground-state and stretchexcited reactions, respectively.

Figure 1. (a) Raw CH3(00) product images (un-normalized) with a superimposed axis indicating the scattering directions; the 0° angle refers to the initial CH4 beam direction in the center-of-mass frame. The lack of cylindrical symmetry of the image is due to the density-toflux correction. The image features are labeled as the correlated product pairs (see text for definition). The three IR-on images P(0,90), P(90,90), and P(90,0) correspond to , IR pointing along the z-, y-, and x-axis, respectively, in the scattering frame. (b) Definition of the scattering frame (see text for details).

To have a clear picture of the polarization dependences of the three IR-on images, Figure 1b depicts the scattering coordinate2,3 used in data analysis. The scattering plane xz is defined by the reactant relative velocity k (the z-axis) and the product recoil direction k′; θ is the product scattering angle. The polarization direction (, IR ) of the IR laser is specified by the polar and azimuthal angles (α, φ) in the scattering frame. Experimentally, all four beams (two molecular beams, IR-pump, and UV-probe lasers) lie in the xz plane. The y-axis is the product ion time-of-flight (TOF) axis that points toward the image detector, and the time-sliced image registers only the reactive signals P(θ;α,φ) in the xz scattering plane. Hence, the exemplified three IR-on images, labeled as P(α = 0°,φ = 90°), P(90°,90°), and P(90°,0°), correspond to , IR pointing along the three orthogonal axes of z, y, and x, respectively, in the scattering frame. A casual inspection of the three raw images observes that the outer-ring changes from backward-scattering in , IR z to sideways dominance in , IR x and becomes very weak in , IR y . Sensitive dependence of the inner-forward feature on the , IR direction is also notable. Obviously, the title reaction must be highly stereoconstrained, at least compelling enough to be so vividly revealed by the raw images shown in Figure 1a. The degrees of the alignment effects can be quantified by systematically rotating the IR polarization direction with all other experimental conditions intact. Figure 2 illustrates the results of the four rotational branches under the same molecular beam geometry. In this α geometry, both molecular beams were simultaneously rotated to make k perpendicular to the propagation axis of the IR laser. As the IR wave plate is rotated, the , IR will be swung between being parallel (α = 0°) and perpendicular (α = 90°) to k (or z), while the azimuthal angle φ remains at 90°, that is, the value of φ is irrelevant.3,4 We denoted the dependency of signals on the IR polarization angle as P(α,90°). Two remarks are worth noting. First, the wellseparated (00,0)s and (00,1)s pairs display a striking out-ofphase dependency on α. For the (00,1)s pairs, a slightly different behavior between its sharp forward peak and the remaining part of the (00,1)s pair was also noted. Therefore, three sets of data were analyzed and labeled as ν0 for the (00,0)s product pair, 3879

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Figure 3. As Figure 2, except that α is kept at 90° and the polarization angle now corresponds to the φ angle in the scattering frame. Note the little polarization dependency of the sharp forward feature, shown by ν1(0−10°) in blue, for all four branches.

Figure 2. Polarization angle dependence of the product signals from the stretch-excited reaction. The initial relative velocity (k) is perpendicular to the IR laser propagation direction and φ = 90°. Thus, varying the IR polarization direction corresponds to changing the angle α with φ invariant in the scattering frame. The ν = 0 data (black) represent the outer-ring feature; for the ν = 1 data, either forward signals within the ±55 (red) or ±10° (blue) cones are counted to elucidate the distinct dependence of the sharp forward peak. For each curve the value of P(α = 0°)/P(α = 90°) is given, indicating the degree of the alignment effects. The dramatically different behaviors of the four rotational-selected states are striking.

reactivity seems to be the vibrational amplitude, not the alignment of the rotational angular momentum or the direction of a particular C−H bond. The last assertion sounds intriguing and yet disconcerting in that it defies the geometric structure concept of the transition state theory, in which a collinear Cl− H−C configuration is favored and thus the bond axis alignment would be inferred. On the other hand, a null alignment effect for P(1) excitation was observed. The state prepared possesses one unit each of rotational (N) and vibrational (l) angular momentum, with a null total angular momentum (J = 0), that is, the rovibrational wave function being isotropic in space. It will instead suggest the J direction as a dominant factor. Before we proceed further, let us elaborate a bit more about the alignments of various angular momenta of CH4(ν3 = 1), excluding the nuclear spin for the time being. Because l = 1 for ν3 = 1 and J = N + l, N can take on the three values of J − 1, J, and J+1, corresponding to l being parallel, perpendicular, and antiparallel to J in the classical vector model.6 The degeneracy of three states is removed by the Coriolis interactions, leading to the three energy levels of F−(J), F0(J) and F+(J) for the R, Q, and P branches, respectively.6 Among the three split states, the state F0(J), with l being perpendicular to J, does not change the frequency. The other two, F−(J) and F+(J) with l being parallel or antiparallel to J, are linear combinations of the original two vibrations and thereby execute in-phase excitations constituting an ensemble of elliptical motions (one clockwise and the other counterclockwise). The above picture depicts the relative directions of J, N, and l in a body-fixed (or molecule-fixed) frame. When CH4 is excited by a linearly polarized IR laser, ν3 = 1 ← 0, the electric field , IR aligns the transition dipole moment d in space, d , IR . The Coriolis constant :3 (= 0.055) for CH4(ν3 = 1) has a positive value,6 and thus, the direction of rotation of d during the vibration coincides with the vibrational angular momentum l, that is, l ⊥ d (or , IR ). In the case of Q transition, one has l ⊥ J in the body-fixed frame, as just mentioned; thus, J , IR (or d) in the space-fixed frame. As for the P/R transition, l ∥ J in the body-fixed frame; then, J ⊥ , IR

ν1(0−55°) and ν1(0−10°) for the (00,1)s pair scattered within the θ = ±55 and ±10° cones, respectively. Second, using the explicit P(α,φ) expression given in the previous reports,2−4 one can readily show that P(α,90°) should behave as a(1 + b cos2 α); a and b are constants. Indeed, all data display such dependencies on α, as demonstrated by the fitted lines. For convenience, a single parameter of P(α = 0°)/P(α = 90°) was used to quantify the polarization dependences, as indicated in the figure. Obviously, P(0°)/P(90°) = 1 means no polarization dependency, whereas the larger deviation from unity indicates a stronger alignment effect. Similarly, in the φ geometry where k is along the IR laser propagation axis, the rotation of the IR wave plate results in a change of the angle φ (Figure 1b) with α kept at 90°.2−4 The dependency of observed signals will then correspond to P(90°,φ), as presented in Figure 3. Intriguingly, the ν0 and ν1(0−55°) channels now display an in-phase variation with IR polarization angles, yet the sharp forward peak of ν1(0−10°) appears nearly invariant to the IR polarization direction. Again, one can readily show that the φ dependency follows the form of c(1 + d cos2 φ), as seen by the fitted lines. The resultant P(0°)/P(90°), with the angles now referred to φ, are also given in the figure. In both α and φ geometries, the observed alignment effects descend in the order of R(0) > R(1) > Q(1) > P(1), exactly the same as the Cl + CHD3(ν1 = 1) reaction.1 It is remarkable that the R(0) excitation yields the most prominent steric effects on reactivity. The prepared state, |1 0 1⟩, is rotationless (N = 0) and thus characterized by a spatially isotropic rotational wave function, for which any orientation of the hydrogen atoms is equally probable. However, the net C− H vibrational amplitude is aligned in space by laser excitation.1,9,10 Hence, the key factor in governing the steric 3880

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(or d) in the space-fixed frame. The distinctive J alignment in space by the Q or P/R transition of CH4(ν3 = 1) can also be understood from the polarization selection rule of ΔmJ = 0 (but not allowed for ΔJ = 0 and m = 0),6 where the quantization axis refers to the , IR axis. It is instructive to contrast the CH4(ν3 = 1) case to CHD3(ν1 = 1). The IR excitation via the Q branch preferentially aligns the angular momentum N for CHD3 or J for CH4 along the , IR direction. When excited by the P/R transition, the N for CHD3(ν1 = 1)1,9,10 or J for CH4(ν3 = 1) is preferentially aligned perpendicular to , IR . The fact that the observed steric effects of the four rotational branches in Cl + CH4(ν3 = 1) show the same propensity as that in Cl + CHD3(ν1 = 1) will suggest that the key factor of our concern should be the IRinduced alignments of N (for CHD3) and J (for CH4). In retrospect, one could have reached the same conclusion more elegantly by recognizing that the IR-induced alignment is acted on the rovibrational angular momentum of the excited molecules, namely, on N for CHD3(ν1 = 1) and J for CH4(ν3 = 1). Because our IR laser does not resolve the hyperfine structures of each rotational transition, the initially aligned CH4(ν3 = 1) reactants are prone to depolarization of alignment due to the coupling of the aligned J to the randomly oriented nuclear spin (I) of the four hydrogen atoms to form the total angular momentum F. This coupling causes the splitting of the rotational levels into hyperfine levels, and the precession of J about F then decreases the degree of alignment in the excited molecular ensemble.19 [Note that the extraction field of ∼25 V/cm in our time-sliced product imaging setup is too weak to decouple J from I, thus to defeat the hyperfine depolarization effects.20] In the time-dependent picture, if the laser excitation of a molecule to a particular rotational sublevel |J mJ⟩ occurs without hyperfine resolution, a coherent superposition of hyperfine sublevels associated with |J mJ⟩ results.21 The result of subsequent time evolution is oscillatory population transfer between the different mJ sublevels, and this beating is the socalled hyperfine depolarization21 as it leads to reducing the degree of polarization of the J distribution. The hyperfine quantum beat has been beautifully demonstrated in a number of studies22−24 and can be characterized by a time-dependent depolarization coefficient Gk(t), which accounts for the evolution of the instantaneous reactant polarization occurring at time t after the initial IR excitation. To investigate the effect of such hyperfine depolarization on the observed steric effect, the temporal profiles of the product images were measured. Figure 4 presents the result of the R(0) excitation under the α geometry. Two polarizations with , IR parallel to k, P(0°,90°), and perpendicular to k, P(90°,90°), are shown, with the two product pairs, (00,0)s and (00,1)s, presented in the upper and lower panels, respectively. In all cases, the signals rise initially with the time delay between two lasers (indicative of the buildup of reaction products) and then decline with further delay as the products fly out of the probe region (which is the origin of the density-to-flux correction17,25). Within the experimental uncertainties, no oscillatory behaviors were seen. Given that, we then approximated the temporal profile by a simple kinetics model. Assuming that the hyperfine depolarization decays exponentially,26 the rate of product formation can be expressed as

Figure 4. Dependence of the CH3(00) signal on the time delay between the IR-pump and the UV-probe lasers under two polarization configurations, ∥ (or P(0°,90°), in red) and ⊥ (or P(90°,90°), in black). The red and black lines are the fits using a simple kinetics model (see text). The kp/kd values used are 2.0, 0.5, and 1.25 for HCl(ν = 0) ∥, HCl(ν = 0) ⊥ (and HCl(ν = 1) ∥), and HCl(ν = 1) ⊥, respectively. The upper panel is for the concomitantly formed HCl(ν = 0), and the lower panel is for HCl(ν = 1). Blue curves show the temporal profiles of the differential signals between the two polarization configurations (∥ and ⊥), with the maximum (the shaded area) occurring near ∼5 ± 1 μs.

dn(t ) n(t ) = k pn0e−t / τ + kdn0(1 − e−t / τ ) − dt τ′

(1)

where τ denotes the characteristic depolarization lifetime, τ′ is the average residence time of the products in the probe zone, kp (kd) gives the apparent rate constant of the polarized (depolarized) reactants, and n0 is the effective concentrations of the initially aligned CH4(ν3 = 1) and the Cl atom. Therefore, the first term in eq 1 accounts for the vibrationally excited reactivity of the aligned reagent, the second term is for the depolarized reactant, and the last term is for the product flying out of the probe region. Solving eq 1 under the initial condition of n(t) → 0 as t → 0, one obtains ⎡ ⎤ ((k p/kd) − 1) n(t ) = kdn0⎢τ′(1 − e−t / τ ′) + (e−t / τ − e−t / τ ′)⎥ ⎢⎣ ⎥⎦ ((1/τ′) − (1/τ )) (2)

Among the four parameters in eq 2, kp and kd are basically the scaling factors and do not yield the actual reaction rates for lack of the density-to-flux corrections.17,25 The temporal dependencies are mainly governed by the reactant depolarization lifetime (τ) and the product residence time (τ′). The IR laser pulse was a few nanoseconds in width, and each pulse illuminated about an 8 mm long region of the CH4 beam.3 After the IR excitation, the excited CH4(ν3 = 1) would travel through the Cl beam, yielding the reaction products. The effective concentration of the two overlapped reactants, n0, becomes a function of time. We modeled this by dividing the excited CH4(ν3 = 1) into about 12 (or more) segments, with 3881

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each described by eq 2. As the ith segment (i = 1−12) passes through the Cl beam (at ti), no more products can be formed by this segment, and only the escape term (the third term in eq 1) remains. Hence, the temporal profile afterward is modeled by n(t ) = n0(ti)e−(t − ti)/ τ ′

for t > ti

presented as to the choices of the rotational branch when preparing the aligned CH4(ν3 = 1) reactants, the optimal time delay between the IR-pump and the UV-probe lasers, and the resultant depolarization correction factor Gk in data analysis. With this information in hand, we have acquired the necessary images to determine a full set of PDDCSs in the Cl + alignedCH4(ν3 = 1) reaction. These data are currently under analysis and will be reported in the future.

(3)

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The observed temporal profiles shown in Figure 4 are the sum of the contributions from those 12 segments, with each described by eq 2 for t = 0−ti and eq 3 for t > ti. The black and red curves shown in Figure 4 are the fitted results, with the fitting parameters τ = 20 μs for all four data sets, τ′ = 3 μs for ν = 0, and τ′ = 4.5 and 5 μs for ν = 1 (⊥) and ν = 1 (∥), respectively. Due to the nature of multiparameter fitting, the fitted values of the parameters are correlated and associated with considerable uncertainties. Nevertheless, the fitted τ = 20 ± 5 μs for CH4(ν3 = 1) is in good agreement with that from the previous report9,27 of 15 μs, as well as an estimate based on the hyperfine splitting of 60−90 kHz.28 Compared to τ ≈ 5 ± 1 μs for CHD3(ν1 = 1),3 the present hyperfine depolarization rate is slower. The blue lines in Figure 4 are the differential signals between the two fitted curves. As seen, for both HCl(ν = 0) and HCl(ν = 1) channels, the differential reactivity peaks near 5 μs of the delay between the IR and UV lasers, which represents the optimal timing that balances the signal buildup and the depolarization of aligned reagents. To estimate the depolarization correction factor at a delay time Δt, we first note that for a reaction with an optically aligned reactant that is initiated at t = 0 and observed at a later time Δt, an effective (or cumulative) hyperfine-depolarization coefficient should be of concern. This is because individual reaction events occur with equal probability throughout the time range, and reactants consumed at early times undergo hyperfine depolarization for a shorter time than those reacted at later times. Hence, we have Gk(Δt) = ⟨n(Δt)⟩/n0, with ⟨n(Δt)⟩ denoting the time-averaged, aligned CH4(ν3 = 1) over the time period from 0 to Δt, that is Δt n τ(1 − e−Δt / τ ) 1 n 0 e −t / τ d t = 0 Δt 0 Δt ⎛ ⎞ t Δ ⎟ ≃ n 0 ⎜1 − ⎝ 2τ ⎠

⟨n(Δt )⟩ =

Corresponding Author

*E-mail: [email protected]. Present Addresses §

(J.Y.) State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian 116023, Liaoning, China. ∥ (F.W.) Department of Chemistry, Fudan University, Shanghai 200433, China. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Dr. Y. Cheng and Q.-Y. Chang for assisting the measurements. This work was supported by the Minister of Science and Technology of Taiwan (MOST 102-2119-M-001) and Academia Sinica.

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REFERENCES

(1) Wang, F.; Lin, J.-S.; Liu, K. Steric Control of the Reaction of CH Stretch-Excited CHD3 with Chlorine Atom. Science 2011, 331, 900− 903. (2) Wang, F.; Liu, K.; Rakitzis, T. P. Revealing the Stereospecific Chemistry of the Reaction of Cl with Aligned CHD3(ν1=1). Nat. Chem. 2012, 4, 636−641. (3) Wang, F.; Lin, J.-S.; Liu, K. How to Measure a Complete Set of Polarization-Dependent Differential Cross Sections in a Scattering Experiment with Aligned Reagents? J. Chem. Phys. 2014, 140, 084202. (4) Wang, F.; Liu, K. Steric Effects in the Cl + CHD3(ν1=1) Reaction. Chin. J. Chem. Phys. 2013, 26, 705−709. (5) Aldegunde, J.; de Miranda, M. P.; Haigh, J. M.; Kendrick, B. K.; Saez-Rabanos, V.; Aoiz, F. J. How Reactants Polarization Can be Used to Change and Unravel Chemical Reactivity. J. Phys. Chem. A 2005, 109, 6200−6217. (6) Herzberg, G. H. Infrared and Raman Spectra of Polyatomic Molecules; Van Nostrand Reinhold: New York, 1945. (7) Kais, S.; Levine, R. D. Directed States of Molecules. J. Phys. Chem. 1987, 91, 5462−5465. (8) Brouard, M.; Chadwick, H.; Eyles, C. J.; Aoiz, F. J.; Klos, J. The k−j−j′ Vector Correlation in Inelastic and Reactive Scattering. J. Chem. Phys. 1995, 135, 084305. (9) Yoder, B. L.; Bisson, R.; Beck, R. D. Steric Effects in the Chemisorption of Vibrationally Excited Methane on Ni(100). Science 2010, 329, 553−556. (10) Simpson, W. R.; Rakitzis, T. P.; Kandel, S. A.; Orr-Ewing, A. J.; Zare, R. N. Reaction of Cl with Vibrationally Excited CH4 and CHD3: State-to-State Differential Cross Sections and Steric Effects for the HCl Product. J. Chem. Phys. 1995, 103, 7313−7335. (11) Chang, Y.; Pan, H.; Wang, F.; Liu, K. On the Signal Depletion Induced by Stretching Excitation of Methane in the Reaction with the F Atom. Phys. Chem. Chem. Phys. 2014, 16, 444−452. (12) Hudgens, J. W.; DiGiuseppe, T. G.; Lin, M. C. Two Photon Resonance Enhanced Multiphoton Ionization Spectroscopy and State Assignments of the Methyl Radical. J. Chem. Phys. 1983, 79, 571−582.

∫

(4)

Then ⎛ Δt ⎞⎟ G k (Δt ) ≃ ⎜1 − ⎝ 2τ ⎠

AUTHOR INFORMATION

(5)

For τ = 20 ± 5 μs and Δt = 5 μs, eq 5 yields Gk(Δt) = 0.88 ± 0.04. Previously, we used an empirical method by plotting the ratios of the two corresponding temporal profiles as a function of t.1 Approximating a linear dependence in the short-time range, the desired Gk was obtained from the intercept at t = 0 and the slope. Applying this approach to the present case, we derived Gk = 0.88 ± 0.03 for HCl(ν = 0) and 0.90 ± 0.03 for HCl(ν = 1) at Δt = 5 μs. Taking all together, we estimated Gk = 0.89 ± 0.02 at Δt = 5 μs, which can be compared with the Gk(Δt = 3.5 μs) = 0.73 ± 0.03 for CHD3(ν1 = 1).2−4 It should be noted that different upper rotational states could exhibit different hyperfine depolarization properties. In order to measure PDDCSs in a scattering experiment with optically aligned reagents, a number of experimental questions need to be addressed first. In this Letter, detailed accounts are 3882

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The Journal of Physical Chemistry Letters

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(13) Shiu, W.; Lin, J. J.; Liu, K.; Wu, M.; Parker, D. H. Imaging the Pair-Correlated Excitation Function: The F + CH4 → HF(ν′) + CH3(ν = 0) Reaction. J. Chem. Phys. 2004, 120, 117−122. (14) Shiu, W.; Lin, J. J.; Liu, K. Reaction Resonance in a Polyatomic Reaction. Phys. Rev. Lett. 2004, 92, 103201. (15) Kawamata, H.; Zhang, W.; Liu, K. Imaging the Effects of the Antisymmetric Stretch Excitation of CH4 in the Reaction with F Atom. Faraday Discuss. 2012, 157, 89−100. (16) Kawamata, H.; Liu, K. Imaging the Nature of the Mode-Specific Chemistry in the Reaction of Cl Atom with Antisymmetric StretchExcited CH4. J. Chem. Phys. 2010, 133, 124304. (17) Lin, J. J.; Zhou, J.; Shiu, W.; Liu, K. Application of Time-Sliced Ion Velocity Imaging to Crossed Molecular Beam Experiments. Rev. Sci. Instrum. 2003, 74, 2495−2500. (18) Zhou, J.; Zhang, B.; Lin, J. J.; Liu, K. Imaging the Isotope Effects in the Ground State Reaction of Cl + CH4 and CD4. Mol. Phys. 2005, 103, 1757−1763. (19) Zare, R. N. Angular Momentum; John Wiley & Sons: New York, 1988. (20) Loesch, H. J.; Stienkemeier, F. Steric Effects in the State Specific Reaction Li + HF(ν=1, j=1, m=0) → LiF + H. J. Chem. Phys. 1993, 98, 9570−9584. (21) Altkorn, R.; Zare, R. N.; Greene, C. H. Depolarization of Optically Prepared Molecules by Two Randomly Oriented Spins. Mol. Phys. 1985, 55, 1−8. (22) Bartlett, N. C.-M.; Miller, D. J.; Zare, R. N.; Alexander, A. J.; Sofikitis, D.; Rakitizs, T. P. Time −Dependent Depolarization of Aligned HD Molecules. Phys. Chem. Chem. Phys. 2009, 11, 142−147. (23) Orr-Ewing, A. J.; Simpson, W. R.; Rakitzis, T. P.; Zare, R. N. Preparing Reagents: Time Dependence of HCl(ν = 1, J) Alignment Following Pulsed Infrared Excitation. Isr. J. Chem. 1994, 34, 95−102. (24) Costen, M. L.; Hall, G. E. Hyperfine Quantum Beats From Photolytic Orientation and Alignment. Phys. Chem. Chem. Phys. 2005, 7, 1408−1413. (25) Sonnenfroh, D. M.; Liu, K. Number Density-to-Flux Transformation Revisited: Kinematic Effects in the Use of Laser-Induced Fluorescence for Scattering Experiments. Chem. Phys. Lett. 1991, 176, 183−190. (26) In principle, a full account of hyperfine depolarization of reactants should consider the superimposed quantum beats,21−24 for which partial alignment could be retained even after long delay time. However, the temporal profile shown in Figure 4 refers to the reaction products and thus is the result of a cumulative depolarization effect (i.e., not the instantaneous time-dependent alignment of the reactants; see eqs 4 and 5) over the delay time of two lasers. In addition, possible collision-induced depolarization effects that tend to damp the oscillatory behaviors cannot be completely ruled out at longer delay time even under the crossed-beam conditions. In conjunction with the fact the observed temporal profiles do not show any oscillation (Figure 4), we surmise that using a more complicated, oscillatory decay form will not significantly affect the estimate made in this work. (27) Yoder, B. L.; Bisson, R.; Hundt, P. M.; Beck, R. D. Alignment Dependent Chemisorptions of Vibrationally Excited CH4(ν3) on Ni(100), Ni(110) and Ni(111). J. Chem. Phys. 2011, 135, 224703. (28) Hall, J. L.; Borde, C. Measurement of Methane Hyperfine Structure Using Laser Saturated Absorption. Phys. Rev. Lett. 1973, 30, 1101−1104.

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dx.doi.org/10.1021/jz502088c | J. Phys. Chem. Lett. 2014, 5, 3878−3883